West is set to portray Croft's father, known as Richard James Croft in the video games, according to Variety.
Directed by Roar Uthaug, the film also stars Walton Goggins and Daniel Wu in unspecified roles.
The reboot will follow the dual pistol wielding adventurer as she sets out on her first expedition to clear her father's disgraced name notes The Hollywood Reporter.
Previously, Vikander stated that the film would be "based on the reboot of the game from 2013."
"That is more of an origin story. You get into an emotional aspect of getting to know Lara hopefully in an in-depth way. So I hope that doing a film of the rebooted game will bring something new and fresh that'll stand on its own two legs," she said of the source material.
The video game series, which has sold over 35 million units, first debuted in 1996 for the original Playstation. The latest series which includes 2013's Tomb Raider and 2015's Rise of the Tomb Raider feature a younger, less experienced, more realistic Lara Croft as she continues to explore the world in the search for treasure much in the same vein as Indiana Jones.
Angelina Jolie famously portrayed the heroine in 2001's Lara Croft: Tomb Raider and again in 2003's Lara Croft Tomb Raider: The Cradle of Life.